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It's 33, 32, it's only 32 times and you can check that math at home but here lies the power of algorithmic thinking, of computational thinking as they say.
你需要33，32，对，32次,你也可以在家里自己计算，但数学算法的力量是无穷的，这就是科学家们所谓的计算机思维。
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so I'll need to do math and science classes for the rest of my college career.
所以我必须在我余下的学生阶段完成数学和自然科学的课程。
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Well, the infinity mechanism, and many of you will be familiar with this from mathematics or computer science, is recursion.
这种无限机制是递归的,你们许多人会在数学与计算机科学中,熟悉这个词
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But, you know, I know someone who was a teacher in a Chicago public school for decades and lost his job, teaching math to high school kids, because he is gay.
我认识一个任职于,一所芝加哥公立学校几十年的老教师,被解雇了，他在高中教数学，仅仅是因为他是同性恋。
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Okay, not to dwell too much on math because you can very quickly bore someone in computer science by dwelling too much on math but it's useful even for logical constructs as we'll see with loops.
不要过于纠结于这些数学问题了,在计算机领域，你会很讨厌那些,在这上面钻牛角尖的人，但是对于那些,像循环这样的逻辑结构又是很有用的。
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He was trying to describe electrons, but the theory said there are two roots in the quadratic equation and the second root is mathematically as interesting as the first one.
他当时只是想去描述电子,但是数学理论告诉我们,二次方程有两个根,而第二个根在数学上和第一个根一样有趣
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Let's do the math here.
我们在这里做数学。
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Others though, I want to tell you that it doesn't-- if you're shopping-- I had a student come by yesterday and ask he's a little rusty in his math skills if he should take this course.
其他的,我想告诉你们不必...,如果你还在挑选课程...,昨天有个学生来问我,他的数学有点荒废了,他该不该选这门课
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So in my first year, I took math, I took English, I took architecture.
所以在第一年里，我上了数学、英语、建筑方面的课。
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And in particular, I'm going to cheat slightly I'm going to use a little bit of abusive mathematics, but I'm going to show you a trick to figure it out.
尤其要说明的是,我会有一点不属实在里面,我会滥用一点数学，但是,我会教会你们这个小把戏的。
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So you can see that we're starting to have a very complicated equation, and it turns out that it's mathematically impossible to even solve the exact Schrodinger equation as we move up to higher numbers of electrons.
所有你们可以看到我们得到了,一个非常复杂的方程，结果是它在数学上是,不可能解出确定的,薛定谔方程,当我们考虑更高的电子数目的时候。
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Again, don't worry too much about the equation, we're not really going to do any math here, I'm just putting it in for completeness.
对这个方程也不需要太深究,在这里我们不强调数学运算的,我把它写出来是为了表述完整
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There're also changes of what you can teach, extends what you can teach, because you can get to concept which are really quite sophisticated that you will never teach it at the introductory level, because the math is the least that you can make it quantitatively, because you have a visualization that shows physically what's going on.
同时这也能改变,教学内容，你能教授的程度，因为你可以定义,那些通常很难的,你在入门阶段都不会遇到的,抽象阶段，因为数学是你最不能,用定量手段来解决的，因为你有一个直观过程,知道什么正在进行。
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and I left my math notes in someone's car
而我却把自己的数学笔记落在谁的车里了。
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But I know today in my math class, we were learning about the guys who created RSA Public Key Cryptography.
但是今天的数学课上，我们在学习RSA公钥加密算法的创始人。
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I talked about life is not like a mathematic problem ? with you or in my other class ?
我说过生活不是个数学难题,是跟你们说过？，还是在我另外的课上？
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The mathematical theory of probability was unknown until that time and you can see that insurance suddenly made an appearance at that time.
在那之前,概率的数学理论,是不存在的,而随着概率论的出现,保险业也突然出现了
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In math, when you see multiple value solutions, these are eigenvalues.
在数学中，当你看到许多值的解法时，这些就是特征值。
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Mathematicians have luckily told us how to analyze the mathematics in any number of dimensions.
数学家们正好告诉了我们,如何在任意维度下进行数学分析
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In that autistic people show no impairments dealing with the physical world, they show no impairments on-- they don't necessarily show any impairments on mathematical skills or spatial skills, but they have a lot of problems with people.
因为孤独症患者并未表现出生理上的缺陷,所以他们并不会在数学技能或空间技能上,表现出什么缺陷,但他们却在人际交往方面存在很多问题
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The so called binary system, 1 these zeros and ones that you'd probably have some vague sense underlie all computers today actually reduced to the exact same grade school kind of math and system except with computers, 1 because it's a lot easier to use just two digits, zero and one.
所谓的二进制就是，你觉得模糊的0与,在电脑上计算,事实上可以简化为跟小学数学一样,只是在电脑上计算而已，因为它更容易，仅仅使用两个数字，0与。
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It is true mathematically, you can add two numbers, but you've got to ask yourself,"What am I doing as a physicist when I add these two numbers?"
在数学上它是正确的,你可以引入这两个常数,但是你需要问问自己,当我引入这两个常数时,这么做有什么物理意义
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Mathematically, we can make it 0.
在数学上讲,我们把它变成零
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The way the physics works is you will find some laws of motion in mathematical form, you put in the initial conditions of whatever, you solve the equations, and the answer that comes, you have no choice.
在物理问题中,你可以用数学方法得到运动定律,你代入初始条件,然后解方程,获得答案,你别无选择
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Therefore, mathematically at a given time t, we can trade t for v and put it into this formula.
因此,从数学角度来说,在给定的时刻 t,我们可以用 v 来表示 t,并代入这个式子
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Now, unlike high school math or in algebra Z where you call things X and Y and Z, in programming, in computer science, you're actually dealing with humans where it's useful to have a variable name that's more descriptive than X and Y and Z.
不像高中数学或者代数中,称为X和Y和，在程序设计和计算机科学里，你实际上是在和人打交道,在这里有个描述性比xyz更强的,变量名称是很重要的。
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You do have mathematical operators in C and most every language.
在C语言还有一些其他,编程语言里有很多数学符号。
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So, all you will have the opportunity to solve differential equations in your math courses here. We won't do it in this chemistry course. In later chemistry courses, you'll also get to solve differential equations.
你们在数学课中有机会,遇到解微分方程,我们在这化学课里就不解了,在今后的化学课程里，你们也会遇到解微分方程的时候。
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And I think that's very important especially with electromagnetism, which is so numb toward if, so abstract and so much math flowing around.
我觉得这是非常重要的,尤其是对于电磁学来说，它是一门很难懂的，很抽象的学科,包含很多数学在里面。
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They read. And one of the people that was reading this literature was a high school teacher who was teaching mathematics in Basil, Switzerland.
其中一个读过这篇文章的人,是个教高中生的老师,在瑞士的罗勒教数学。
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